Finite Element Approximation for A Convective Brinkman-Forchheimer Problem Coupled with A Heat Equation

被引：1

作者：

Campana, Gilberto ^{[1
]}

Munoz, Pablo ^{[1
]}

Otarola, Enrique ^{[2
]}

机构：

[1] Univ Tecn Federico Santa Maria, Dept Ciencias, Valparaiso, Chile

[2] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso, Chile

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2025年 / 104卷 / 01期

关键词：

Non-isothermal flows; Nonlinear equations; A convective Brinkman-Forchheimer problem; A heat equation; finite element approximations; Convergence; A priori error estimates; DOUBLE-DIFFUSIVE CONVECTION; NUMERICAL DISCRETIZATION; MIXED FORMULATION; NONLINEAR FLOW; NAVIER-STOKES; INERTIA; STEADY; MODEL;

D O I：

10.1007/s10915-025-02932-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate a convective Brinkman-Forchheimer problem coupled with a heat equation. The investigated model considers thermal diffusion and viscosity depending on the temperature. We prove the existence of a solution without restriction on the data and uniqueness when the solution is slightly smoother and the data is suitably restricted. We also propose a finite element discretization scheme for the considered model and derive convergence results and a priori error estimates. Finally, we illustrate the theory with numerical examples.

引用

页数：33

共 72 条

[1]

Adams R.A., 2003, Pure and Applied Mathematics (Amsterdam), V140

[2] SPECTRAL DISCRETIZATION OF THE NAVIER-STOKES EQUATIONS COUPLED WITH THE HEAT EQUATION [J].

Agroum, Rahma ;

Aouadi, Saloua Mani ;

Bernardi, Christine ;

Satouri, Jamil .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2015, 49 (03) :621-639

[3]

Allali K, 2005, INT J NUMER ANAL MOD, V2, P179

[4] Finite Element Discretizations of a Convective Brinkman-Forchheimer Model Under Singular Forcing [J].

Allendes, Alejandro ;

Campana, Gilberto ;

Otarola, Enrique .

JOURNAL OF SCIENTIFIC COMPUTING, 2024, 99 (02)

[5] Darcy's problem coupled with the heat equation under singular forcing: analysis and discretization [J].

Allendes, Alejandro ;

Campana, Gilberto ;

Fuica, Francisco ;

Otarola, Enrique .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2024, 44 (06) :3683-3716

[6] NUMERICAL DISCRETIZATION OF A DARCY-FORCHHEIMER PROBLEM COUPLED WITH A SINGULAR HEAT EQUATION [J].

Allendes, Alejandro ;

Campana, Gilberto ;

Otarola, Enrique .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2023, 45 (05) :A2755-A2780

[7] The stationary Boussinesq problem under singular forcing [J].

Allendes, Alejandro ;

Otarola, Enrique ;

Salgado, Abner J. .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2021, 31 (04) :789-827

[8] Stabilized finite element approximations for a generalized Boussinesq problem: A posteriori error analysis [J].

Allendes, Alejandro ;

Naranjo, Cesar ;

Otarola, Enrique .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2020, 361

[9] A fully mixed finite element method for the coupling of the Stokes and Darcy-Forchheimer problems [J].

Almonacid, Javier A. ;

Diaz, Hugo S. ;

Gatica, Gabriel N. ;

Marquez, Antonio .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2020, 40 (02) :1454-1502

[10] Multifrontal parallel distributed symmetric and unsymmetric solvers [J].

Amestoy, PR ;

Duff, IS ;

L'Excellent, JY .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2000, 184 (2-4) :501-520

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